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Integrate the functions((1+logx)^2)/x...

Integrate the functions`((1+logx)^2)/x`

Text Solution

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Let `1+logx=t`
Differentiating both sides w.r.t x
`0+1/x=dt/dx`
`1/x=dt/dx`
`dx=x.dt`
`int (1+logx)^2/x.dx`
Putting `1-logx=t`and `dx=x.dt`
`int t^2/x.x.dt`
`int t^2.dt`
`t^(2+1)/(2+1)+C`
`t^3/3+C`
`1/3(1+logx)^3+C`
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